Abstract
Shape-invariant potentials in the sense of Gendenshteïn (1983 JETP Lett. 38 356) which depend on more than two parameters are not known to date. Cooper et al (1987 Phys. Rev. D 36 2458) posed the problem of finding a class of shape-invariant potentials which depend on n parameters transformed by translation, but it was not solved. We analyse the problem using some properties of the Riccati equation and find the general solution.